The physics of many-body systems strongly depends on their dimensionality. For example, in a two-dimensional world, most standard phase transitions towards an ordered state of matter would not occur because of the increased role of fluctuations. However, non-conventional "topological" transitions can still take place, as understood initially by Kosterlitz and Thouless who were awarded the 2016 Physics Nobel prize for their work.

During the last decade, a novel environment has been developed for the study of low-dimensional physics. It consists of cold atomic gases confined in tailor-made light traps, forming thus a thin layer of material particles. In this talk I will present some key aspects of these quantum 2D gases, such as their transition to a superfluid state. I will also address other topology-related effects in these systems, in relation with the creation of artificial gauge fields and quantum-Hall type phenomena.